# -*- coding: utf-8 -*-

"""剑指 Offer II 013. 二维子矩阵的和
给定一个二维矩阵 matrix，以下类型的多个请求：

计算其子矩形范围内元素的总和，该子矩阵的左上角为 (row1, col1) ，右下角为 (row2, col2) 。
实现 NumMatrix 类：

NumMatrix(int[][] matrix) 给定整数矩阵 matrix 进行初始化
int sumRegion(int row1, int col1, int row2, int col2) 返回左上角 (row1, col1) 、右下角 (row2, col2) 的子矩阵的元素总和。 

示例 1：
输入: 
["NumMatrix","sumRegion","sumRegion","sumRegion"]
[[[[3,0,1,4,2],[5,6,3,2,1],[1,2,0,1,5],[4,1,0,1,7],[1,0,3,0,5]]],[2,1,4,3],[1,1,2,2],[1,2,2,4]]
输出: 
[null, 8, 11, 12]

解释:
NumMatrix numMatrix = new NumMatrix([[3,0,1,4,2],[5,6,3,2,1],[1,2,0,1,5],[4,1,0,1,7],[1,0,3,0,5]]]);
numMatrix.sumRegion(2, 1, 4, 3); // return 8 (红色矩形框的元素总和)
numMatrix.sumRegion(1, 1, 2, 2); // return 11 (绿色矩形框的元素总和)
numMatrix.sumRegion(1, 2, 2, 4); // return 12 (蓝色矩形框的元素总和) 

提示：
m == matrix.length
n == matrix[i].length
1 <= m, n <= 200
-10^5 <= matrix[i][j] <= 10^5
0 <= row1 <= row2 < m
0 <= col1 <= col2 < n
最多调用 10^4 次 sumRegion 方法"""


class NumMatrix:
    """因为同一个矩阵可能会被多次范围求和，所以对每行进行前缀和"""
    def __init__(self, matrix):
        self.matrix = matrix
        self.presums = self.sumPresumsPerRow()

    def sumPresumsPerRow(self):
        presums = []
        for row_li in self.matrix:
            presums_row = [0]
            for col_num in row_li:
                presums_row.append(presums_row[-1]+col_num)
            presums.append(presums_row)
        return presums

    def sumRegion(self, row1: int, col1: int, row2: int, col2: int) -> int:
        col1 += 1
        col2 += 1
        total = 0
        for row in range(row1, row2+1):
            presums_li = self.presums[row]
            total_row = presums_li[col2]-presums_li[col1-1]
            total += total_row
        return total


# Your NumMatrix object will be instantiated and called as such:
# obj = NumMatrix(matrix)
# param_1 = obj.sumRegion(row1,col1,row2,col2)

if __name__ == '__main__':
    numMatrix = NumMatrix([[3,0,1,4,2],[5,6,3,2,1],[1,2,0,1,5],[4,1,0,1,7],[1,0,3,0,5]])
    print(numMatrix.sumRegion(2, 1, 4, 3))
    print(numMatrix.sumRegion(1, 1, 2, 2))
    print(numMatrix.sumRegion(1, 2, 2, 4))
